Actually, it may seem like it is an Apple II "emulator" because of the way it behaves, but clearly it is NOT since it actually uses the same processor as the as the Apple II. What seems clear to me is that the software required to initialize the III to run Apple II software, was more of an inhibitor/limiter as I already related it to Apple's OS X Boot Camp to run Windows on an Intel processor. But perhaps a more apt comparison is to look at efforts to put OS X on a PC. Apple has intentionally crippled the software so it will not install on a PC, despite the fact it runs perfectly well on the exact same processors. It is my understanding that Apple intentionally installed similar, but hardware traps in the III to interrupt an Apple II direct boot, and therefore the limited use of the II software had to be "enabled" via software which also defined the restrictions of the expansive hardware otherwise available to it. It seems like it only "emulated" a II in the sense it forced the more advanced hardware to behave in a more limited fashion. The fact that cards were later developed to overcome the Apple II limited operation capabilities, seems to indicate a hardware issue rather than a software one.
When you say the Apple III won't run a lot of Apple II software, do you mean software available in 1980, or software later developed for the IIe?
Also, could you stick a boot disk from a IIe into a IIGS and it would start up without any other assistance?
Ah, so what you are saying is, unlike the RISC PowerPC chips which literally had the 68K code "instantaneously" converted by software, the Apple II code on the IIGS actually ran in a sub-section of the 65802, literally dedicated to the 6502 processes, like a Math Co-processor which could be integrated into the CPU or on a separate chip. In which case, the Apple II & Apple III are both Apple II hardware at their cores.
Having said that, after pointing out how Windows and OS X will both run on the same processor at the core of both Macs & PCs, yet are limited by the surrounding hardware, I suppose the III truly is a different Apple, whereas that integration ensures the IIGS is a II. However, by that same token, Running Windows on a Mac, makes the Mac no different than a PC. I suppose the Mega II Card in the IIGS is the difference –– if a similar PC hardware card were added into an expansion slot, then one could call such a machine the "Apple PC".
So the next question is whether Apple III software will run on an Apple IIe?